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JEE Main 202313 AprilEvening Shift
Exam
JEE Main
Year
2023
Date
13 April
Shift
Evening Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2023 · 13 April · Evening Shift · Physics · Mechanical Properties of Fluids

Given below are two statements: one is labelled as Assertion A and...

Given below are two statements: one is labelled as

Assertion A and the other is labelled as Reason R

Assertion A : A spherical body of radius (5±0.1)mm( 5 \pm 0 . 1 ) mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 44 %.

Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below

Options

  1. ABoth A and R are true and R is the correct explanation of A
  2. BBoth A and R are true but R is NOT the correct explanation of A
  3. CA is true but R is false
  4. DA is false but R is true

Correct answer

C. A is true but R is false

Step-by-step solution

The terminal velocity is

VT=29r2g(ρ−ρ′)η⇒VT∝r2{V}_{T} = \dfrac{2}{9}{r}^{2}g\dfrac{\left(ρ - {ρ}^{'}\right)}{η} ⇒ {V}_{T} ∝ {r}^{2}

Differentiating and dividing by VT{V}_{T},

⇒dVTVT=2drr=2×0.15⇒ \dfrac{d{V}_{T}}{{V}_{T}} = 2\dfrac{dr}{r} = 2 \times \dfrac{0 . 1}{5}

So, the percentage error is

dVTVT×100=0.25×100=4\dfrac{d{V}_{T}}{{V}_{T}} \times 100 = \dfrac{0 . 2}{5} \times 100 = 4 %

As can be seen the terminal velocity is directly proportional to the square of the radius. Hence AA is true but RR is false.

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